We report on a NuSTAR and XMM-Newton program that has observed a sample of three extremely luminous, heavily obscured WISE-selected AGN at z~2 in a broad X-ray band (0.1 - 79 keV). The parent sample, selected to be faint or undetected in the WISE 3.4um (W1) and 4.6um (W2) bands but bright at 12um (W3) and 22um (W4), are extremely rare, with only ~1000 so-called W1W2-dropouts across the extragalactic sky. Optical spectroscopy reveals typical redshifts of z~2 for this population, implying rest-frame mid-IR luminosities of L(6um)~6e46 erg/s and bolometric luminosities that can exceed L(bol)~1e14 L(sun). The corresponding intrinsic, unobscured hard X-ray luminosities are L(2-10)~4e45 erg/s for typical quasar templates. These are amongst the most luminous AGN known, though the optical spectra rarely show evidence of a broad-line region and the selection criteria imply heavy obscuration even at rest-frame 1.5um. We designed our X-ray observations to obtain robust detections for gas column densities N(H)<1e24 /cm2. In fact, the sources prove to be fainter than these predictions. Two of the sources were observed by both NuSTAR and XMM-Newton, with neither being detected by NuSTAR and one being faintly detected by XMM-Newton. A third source was observed only with XMM-Newton, yielding a faint detection. The X-ray data require gas column densities N(H)>1e24 /cm2, implying the sources are extremely obscured, consistent with Compton-thick, luminous quasars. The discovery of a significant population of heavily obscured, extremely luminous AGN does not conform to the standard paradigm of a receding torus, in which more luminous quasars are less likely to be obscured. If a larger sample conforms with this finding, then this suggests an additional source of obscuration for these extreme sources.
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